Plate, Transducer and Methods for Making and Operating a Transducer

ABSTRACT

A plate, a transducer, a method for making a transducer, and a method for operating a transducer are disclosed. An embodiment comprises a plate comprising a first material layer comprising a first stress, a second material layer arranged beneath the first material layer, the second material layer comprising a second stress, an opening arranged in the first material layer and the second material layer, and an extension extending into opening, wherein the extension comprises a portion of the first material layer and a portion of the second material layer, and wherein the extension is curved away from a top surface of the plate based on a difference in the first stress and the second stress.

TECHNICAL FIELD

The present invention relates generally to a plate, a transducer andmethods of making and operating a transducer.

BACKGROUND

Generally, a transducer is a device that converts one type of energy toanother. The conversion can be to/from electrical, electro-mechanical,electromagnetic, photonic, photovoltaic, or any other form of energy.While the term transducer commonly implies use as a sensor/detector, anydevice which converts energy can be considered as a transducer.

SUMMARY OF THE INVENTION

In accordance with an embodiment of the present invention, a platecomprises a first material layer comprising a first stress and a secondmaterial layer arranged beneath the first material layer, the secondmaterial layer comprising a second stress. The plate further comprisesan opening arranged in the first material layer and the second materiallayer and an extension shaping the opening, wherein the extensioncomprises a portion of the first material layer and a portion of thesecond material layer, and wherein the extension is curved away from atop surface of the plate based on a difference between the first stressand the second stress.

In accordance with an embodiment of the present invention, a transducercomprises a membrane, a back-plate comprising an opening, the openingcomprising a convex portion, wherein the convex portion is curved towardthe membrane, and a spacer between the membrane and the back-plate.

In accordance with an embodiment of the present invention, a method foroperating a transducer comprises receiving a sound wave at a membrane,moving the membrane toward a back-plate, wherein the back-platecomprises an opening, wherein an extension extends into the opening, andwherein the extension is curved toward the membrane, and generating asignal in response to the moving membrane.

In accordance with an embodiment of the present invention, a method formanufacturing a transducer comprises forming a membrane in a substrateand forming a back-plate comprising a first material layer and a secondmaterial layer, the first material layer comprising a different stressthan the second material layer. The method further comprises forming anopening in the back-plate, the opening comprising an extension extendinginto the opening, wherein forming the opening comprises etching theopening in the first material layer using a first etch process, andetching the opening in the second material layer using a second etchprocess.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention, and theadvantages thereof, reference is now made to the following descriptionstaken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates a cross sectional view of a microphone;

FIG. 2 a illustrates a top view of an embodiment of an opening in theback-plate;

FIG. 2 b illustrates a cross sectional view of the back-plate;

FIG. 2 c illustrates a chart with graphs for different back-platematerial compositions;

FIG. 2 d illustrates the deflection of the extension relative to theback-plate;

FIG. 3 a illustrates an embodiment of a layout of a back-plate;

FIG. 3 b illustrates a top view of an embodiment of an elongatedopening;

FIG. 3 c illustrates an embodiment of a layout of a back-plate;

FIG. 3 d illustrates an embodiment of a layout of a back-plate;

FIGS. 4 a-e illustrate embodiments of layouts of a back-plate;

FIG. 5 illustrates a method for manufacturing a transducer;

FIG. 6 illustrates a method for operating a transducer; and

FIG. 7 illustrates a membrane pushing against the back-plate.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The making and using of the presently preferred embodiments arediscussed in detail below. It should be appreciated, however, that thepresent invention provides many applicable inventive concepts that canbe embodied in a wide variety of specific contexts. The specificembodiments discussed are merely illustrative of specific ways to makeand use the invention, and do not limit the scope of the invention.

The present invention will be described with respect to embodiments in aspecific context, namely a membrane. The invention may also be applied,however, to other devices having a movable element and a fixed element,wherein the movable element moves relative to the fixed element.

Transducers may convert electrical, electro-mechanical, electromagnetic,photonic, photovoltaic energy to another type of energy. For example, atransducer can be a capacitor with a movable electrode. The movableelectrode may move against a fixed electrode resulting in a change ofcapacity between the two electrodes. The change in capacity is providedto an output. The transducer is typically operated by a bias voltage,i.e. a potential which may be adjusted freely to the respectivecircumstances, that is applied between the membrane and the counterelectrode.

The transducer may be a stand alone device or may be connected to asimple application specific integrated circuit (ASIC). Alternatively,the transducer may be integrated in an integrated circuit (IC).

One example of a transducer is a microphone. A microphone converts soundenergy of a sound wave into electrical energy. The movable membrane orelectrode may be mechanically connected to a substrate and has a volumeof air surrounding it. Pressure changes of the sound waves deform ordeflect the membrane. A back-plate or counter-electrode may compriseopenings so that air between the back-plate and the membrane can freelydisplace and the movement of the membrane is not dampened.

A challenge in manufacturing and/or operating a microphone is that themovable membrane should not adhere or stick to the back-plate. Toprevent that, conventional devices may have a coating layer on themovable membrane and/or the back-plate or arrange anti-sticking bumps onthe back-plate to minimize or avoid stiction.

An advantage of an embodiment of the present invention is that stictionin the micro structure is prevented. Another advantage of an embodimentis that the contact area between the membrane and the back-plate isreduced. A further advantage of an embodiment is that the membrane isnot pierced or damaged by bent extensions.

In one embodiment an extension is formed in an opening of theback-plate. The extension may be bent towards the movable membranereducing the potential contact area between the movable membrane and theback-plate. The extension may be in its equilibrium position if nottouched by the membrane and may be displaced from its equilibriumposition if touched by the membrane.

FIG. 1 shows a microphone 100 arranged in or on a support substrate 110.The microphone 100 comprises a back-plate 120 and a membrane 130. Theback-plate 120 is spaced apart from the membrane 130 by a spacer 140.The space between the back-plate 120 and the membrane 130 may be filledwith free air, i.e. with air which does not dampen the movement of themembrane 130. The air is free because openings 139 at opening locations126 in the back-plate 120 let the air exhaust if the membrane 130 movestowards the back-plate 120 and an opening 105 in the support substrate110 let the air exhaust if the membrane 130 moves in the otherdirection, away from the back-plate 120. The back-plate 120 and themembrane 130 may be electrodes. While the back-plate 120 may be a fixedelectrode, the membrane 130 may be a movable electrode.

The back-plate 120 may comprise a first material layer 122 and a secondmaterial layer 124. The first material layer 122 may be a conductivelayer comprising doped polysilicon, a metal, or other conductivematerials. The second material layer 124 may comprise an insulatingmaterial such as a nitride, an oxide or the like. Alternatively, thesecond material layer 124 may comprise a conductive material. The firstmaterial layer 122 may be relatively thick while the second materiallayer 124 may be relatively thin. For example, the first material layer122 may be about 300 nm to about 3000 nm thick, and the second materiallayer 124 may be about 30 nm to about 300 nm thick.

The back-plate 120 may comprise a plurality of openings 139.Conventional back-plates may have perfectly round perforations.Embodiments of the invention provide openings which may not be perfectlyround, which may comprise a convex portion and/or which may comprise oneor more extensions shaping the openings. Layouts of embodiments of theseopenings are disclosed and discussed in FIGS. 2 a-2 b, 3 a-3 d and 4 a-4e. In one embodiment a first opening of the back-plate may feature onetype of opening while a second opening may feature another type ofopening.

The plurality of the openings 139 and extensions 128 may be formed by adouble lithography/etch process. In a first step the first materiallayer 122 may be structured and material may be removed where theopenings are located and in a second step the second material layer 124may be structured and material may be removed in order to finalize theopenings. The extensions 128 may bend automatically when the openingsare formed because of the bimorph character of the combination of thefirst and second material layers 122, 124, e.g., the difference instress in the first and second material layers 122, 124.

The membrane 130 may be as thin as possible so that it will deformsignificantly with slight changes in pressure, e.g., small soundpressure levels. However, the thickness reduction of the membrane 130may be limited because of stability requirements (destruction with toohigh a sound pressure or too high a voltage) and the requirement thatstiction to the back-plate 120 should be prevented. In one example, themembrane 130 may be about 1 mm in diameter and about 3 μm thick.

The membrane 130 may comprise a conductive material such as doped orundoped polysilicon, or the like. The membrane 130 may be arranged to bemovable relative to the back-plate 120. The membrane 130 may bemechanically connected along its circumference to the substrate 110 andmay be electrically contacted to contact pads. The contact pads may bearranged on the substrate 110.

The spacer 140 may comprise an insulating material such as an oxide or anitride. The spacer 140 may comprise a thickness of about 2 μm or lessas an example. The substrate 110 may be a semiconductor substrate suchas bulk silicon, SiGe or the like.

FIG. 2 a shows a layout of an embodiment of the opening locations 126 inthe back-plate 120. An extension 128 extends into the opening 139shaping the opening 139. The extension 128 has the form of a cantileveror beam. FIG. 2 b shows a cross-sectional view along the line A-A. Ascan be seen from FIG. 2 b, the extension 128 is bent away in a directionnormal to a top surface 121 of the back-plate 120.

In an embodiment the material of the first material layer 122 maycomprise a different stress than the material of the second materiallayer 124. For example, the first material layer 122 may have a lowertensile stress than the second material layer 124. Alternatively, thefirst material layer 122 may have a higher compressive stress than thesecond material layer 124. The different stress material layers maycause the extension 128 to bend. The extension 128 may bend towardsmovable membrane 130.

FIG. 2 c shows two different graphs 155/165 for two different materialcompositions 150/160 for the two material layers 122, 124. The twographs 155/165 show bending relative to length of the extension 128. Ina first material composition 150 the first material layer 122 is 330 nmthick, has a stress of 43 MPa, and comprises polysilicon, and the secondmaterial layer 124 is 280 nm thick, has a stress of 1 GPa and comprisessilicon nitride. The first material composition 150 results in graph155. As can be seen from this graph 155, the deflection h for theextension 128 shown in FIG. 2 d is −1130 nm for a beam of 20 μm length.In a second material composition 160 the first material layer 122 is1400 nm thick, has a stress of 100 MPa, and comprises polysilicon, andthe second material layer 124 is 140 nm thick, has a stress of 1 GPa,and comprises silicon nitride. The first material composition 150results in graph 165. As can be seen from this graph 165, the deflectionh for extension 128 is −194 nm for a beam of 20 μm length.

The deflection or bending height h is the difference between the tip 129of the extension 128 and the upper surface of the back-plate 120 as canbe seen from FIG. 2 d. The bending height h is controlled by thematerials of the first and second material layers 122, 124, by thestress of these materials and/or by the length of the extension 128. Ascan be seen from FIG. 2 c any deflection h can be designed by choosingthe correct material composition, stress relations and extension length.

FIG. 3 a shows an embodiment of a layout of a back-plate 120. Theback-plate 120 comprises elongated opening locations 126 arrangedalternately in x-direction and in y-direction. Each elongated openinglocation 126 comprises a beam or cantilever 128 extending into theelongated opening 139. A distance in y-direction from a first centerline 136 of a first elongated opening location 126 to a second centerline 137 of a second elongated opening location 126 is 6 μm. A distancein x-direction from a first end 138 of a first elongated openinglocation 126 to a first end 139 of a second elongated opening location126 is 17.5 μm. The embodiment of FIG. 3 a may allow an easy scaling ofthe elongated opening locations 126 and the cantilever 128. A desireddeflection h may be defined by the length of the cantilever 128. Thelonger the cantilever 128 the higher may be the deflection h. Forexample, a low air damping may be achieved when a deflection h of thecantilever 128 is wider than the thickness of the back-plate 120. Suchan arrangement may be used for microphones 100 in high sensitivityapplications or in high signal to noise ratios applications.

FIG. 3 b shows a top view of an elongated opening location 126 having abeam 128 forming the opening 139. In this example, the beam 128 is 10 μmlong and 5 μm wide. The elongated opening location 126 may be 15 μm longand 6 μm wide. As can be seen from FIG. 3 b the elongated openinglocation 126 has an opening 139. The area of the extension 128 and thearea of the opening 139 together form the area of the opening location126. The plurality of openings 139 generates an effective open area of26% when placed in the back-plate 120 as shown in FIG. 3 a. Theeffective open area is a parameter when calculating the damping of airflowing through these openings 139. The opening 139 comprises a concaveportion 139 a having a radius of 2.5 μm and a convex portion 139 d. Theopening 139 also comprises two holes 139 b having a diameter of 1 μm.The two holes 139 b are connected to the concave portion 139 a viaelongated gaps 139 c, the gaps being 0.5 μm wide. The holes 139 b at theend of the 0.5 μm slot may reduce the stress concentration in adjacentregions surrounding the holes 139 b. Without the holes 139 b there wouldbe an increased notching effect.

FIG. 3 c shows another embodiment of a layout of the back-plate 120. Theback-plate 120 comprises a first region 120 a where a plurality of firstelongated opening locations 126 is aligned in x-direction and a secondregion 120 b where a plurality of elongated opening locations 126 isaligned in y-direction. The first region 120 a may comprise at least 2elongated opening locations 126 and the second region 120 b may compriseat least 2 elongated opening locations 126.

The alignment of the extensions 128 in different directions may beadvantageous in rotational symmetric microphone applications wherein themembrane 130 is round, for example. The membrane 130 typically shows aballoon type bowing when displaced extensively. In the event that themembrane 130 touches the back-plate 120 the curved cantilevers 128 inthe middle of the back-plate 120 are touched first and the curvedcantilevers 128 near the round edge are touched later. The curved beams128 are arranged in radial direction so that in case of a contactbetween the membrane 130 and the curved beams 128 the beams 128 mayexperiences no or almost no movement perpendicular to its elongation.

FIG. 3 d shows another embodiment of a layout of the back-plate 120. Theback-plate 120 comprises a symmetric arrangement of elongated openinglocations 126. The elongated opening locations 126 are all facing towarda center point P. In this particular example, the combined distance ofthree neighboring elongated openings 126 (e.g., measured as the distancein y-direction of FIG. 3 a) is the same as the length of one elongatedopening 126.

FIG. 3 a-3 d show specific examples of how elongated opening locations126 can be arranged in the back-plate 120. However, there are many otherpossible arrangements. For example, the elongated opening locations 126may all be arranged facing in the same direction, e.g., the concaveportions 139 a of the openings 139 are arranged on the left side of theelongated opening locations 126. The elongated opening locations 126 oftwo rows may be parallel shifted or staggered relative to one other. Ina further example, the elongated opening locations 126 may not bearranged in a preferred direction (x- or y-direction) but may berandomly oriented.

FIG. 4 a shows a further embodiment of a layout of an opening location126 in the back-plate 120. The opening location 126 is almost completelycovered by the extension 128. There is only a small opening 149 forminga U. A layout with such a small opening 149 may still provide excellentventilation because the extension 128 is bent and air still cancirculate easily through the opening 149.

The layout of FIG. 4 may be used for applications that need minimumventilation or high air damping. For example, the layout may be used formicrophones for high sound pressure levels. In one embodiment theextension 128 may be relatively short and may bend less than thethickness of the back-plate 120.

FIG. 4 b shows another embodiment of a layout of opening locations 126in the back-plate 120. A top view of the opening location 126 maycomprise an opening 159 of a star. The area of the extensions 128 andthe area of the opening 159 form the area of the opening location 126.In this example, eight extensions 128 shape the opening 159 forming thestar. Each extension 128 may be a triangular cantilever with a roundtip. The gap between two sides of two neighboring extensions 128 is 0.5μm and the length of the gap is 10 μm. An effective open area ofapproximately 13% of the back-plate 120 is formed when the openinglocations 126 are placed in a trigonal grid of 30 μm. Each of the eightextensions 128 may be bent away from the back-plate 120. In oneembodiment the layout of FIG. 4 may be used in an application wherelarge damping is desired.

FIG. 4 c shows another embodiment of a layout of an opening location 126arrangement in the back-plate 120. A top view of the opening location126 may comprise an opening 169 of a star. The area of the extensions128 and the area of the opening 169 form the area of the openinglocation 126. Three extensions 128 shape the opening locations 126forming the star opening 169. Each extension 128 may approximate atriangle with an angle tip. The length from the tip of the triangle tothe circumferential line is 10 μm. The effective open area of openings169 is approximately 37% of the overall back-plate 120 area when theopening locations 126 are placed in a trigonal grid of 30 μm. Comparedto the situation shown in FIG. 4 b this gives a much lower air dampingsince the opening 169 is much wider. Additional holes 169 a between theopening locations 126 may reduce the release etching time of asacrificial layer that is etched away when the membrane 130 and theback-plate 120 are formed.

FIG. 4 d shows another embodiment of a layout of an opening location 126in the back-plate 120. The opening 179 of the opening location 126 has aform of a cloverleaf. The opening location 126 comprises four extensions128 all with the same dimension. The extensions 128 form beams withround tips.

FIG. 4 e shows yet another embodiment of a layout of an opening location126 in the back-plate 120. The central aperture 189 forms a circle.Extensions 128 are created by cutting elongated aperture extension 190into the back-plate material so that the extensions 128 form fins of afish. The layout of FIG. 4 e may be advantageous for layouts where thereis less lateral space so that a spiral like design may help winding oneor several extensions 128 around the central aperture 189.

For embodiments of opening locations 126 with more than one extension128, the extensions 128 may all be bent, or alternatively, only some ofthe extensions 128 may be bent. Moreover, the number of extensions 128for each of the embodiments of the opening locations shown in FIG. 4 a-4e may vary between one and eight, for example.

The effective open area of openings in the back-plate 120 in FIGS. 3 a-3d and 4 a-4 e depends on density of the placement of these openinglocations relative to each other.

FIG. 5 shows a method for manufacturing a transducer. In a first step210 a membrane is formed in the support substrate. In a second step 220a back-plate is formed. In one embodiment, the back-plate may be formedover the support substrate and the membrane. The back-plate may comprisea first material layer and a second material layer. The back-plate maybe formed in a distance from the membrane. In one embodiment, an areabetween the back-plate and the membrane may be filled with a sacrificiallayer and spacers.

In a third step 230, an opening is formed in the back-plate. Anextension may extend into the opening. The extension and the opening maycomprise an embodiment of a layout shown in FIGS. 3 a-3 d and 4 a-4 e.The opening may be formed by etching first the first material layer andthen the second material layer. In one embodiment, the opening may beformed by two different etching steps using different etch chemistries.The form of the opening may be defined by a photoresist. After theetching of the opening is complete, a sacrificial layer may be removedbetween the membrane and the back-plate. This is shown in step 240. Thesacrificial layer may be removed applying a wet-etch chemistry or a dryetch chemistry. The sacrificial layer may be removed through the openingand through additional holes also formed in the back-plate.

The extension of the opening may bend as soon as the opening is formeddue to different stress properties of the first material layer and thesecond material layer.

The steps 210-240 in FIG. 5 may be performed in a different order thandescribed in the previous paragraphs. For example, the sacrificial layermay be removed before the opening is formed.

FIG. 6 shows a method for operating a transducer. In a first step 310the method comprises receiving a sound wave at a membrane. In a secondstep 320 the membrane moves toward a back-plate. The back-plate maycomprise an opening and an extension may shape the opening. Theextension may be curved toward the membrane. The extension and theopening may comprise an embodiment of a layout shown in FIGS. 3 a-3 dand 4 a-4 e. In a third step 330 a signal is generated in response tothe movement of the membrane. In one embodiment, in a fourth step 340the signal may be provided to an output.

The procedures described in connection with FIGS. 5 and 6 may berealized utilizing the previously described implementations.

FIG. 7 shows an operational mode where the movable membrane 130 ispressed against the back-plate 120. Under normal operating conditionsthe membrane 130 may not touch the back-plate 120 or the bent extensions128 of the back-plate 120. However, the operational mode of FIG. 7 mayoccur, for example, in the event of an over pressure, a huge static airpressure change, a shock or drop event, or an electrostatic over voltagecausing a pull-in. The movable membrane 130 may be pressed first againstthe tips 129 of the extensions 128. At a certain predetermined pressure,the extensions 128 may yield to the pressing membrane 130. Theextensions 128 may flatten, moving into their respective openings 199.Under extreme conditions, the extensions 128 may completely move intothe openings 199 so that the top surfaces of the extensions 128 arecoplanar with the top surface 121 of the back-plate 120. The extensions128 may not pierce or destroy the membrane 130.

It is noted that the extensions 128 have a bending height h as describedwith regard to FIG. 2 d. The bending height h may be the result of thetwo different stresses in the first and second material layers 122, 124of the back-plate 120. The extensions 128 having the bending height hmay be formed automatically or at the same time when the openings 199are formed. The extensions 128 find an equilibrium height based on thestress combination in the back-plate 120. The extensions 128 may betemporarily displaced by exerting a force against them, e.g., when themembrane 130 presses against them. They may not break but rather yieldrelative to the pressing force. As soon as the force is removed theextensions return to their old equilibrium position.

Although the present invention and its advantages have been described indetail, it should be understood that various changes, substitutions andalterations can be made herein without departing from the spirit andscope of the invention as defined by the appended claims.

Moreover, the scope of the present application is not intended to belimited to the particular embodiments of the process, machine,manufacture, composition of matter, means, methods and steps describedin the specification. As one of ordinary skill in the art will readilyappreciate from the disclosure of the present invention, processes,machines, manufacture, compositions of matter, means, methods, or steps,presently existing or later to be developed, that perform substantiallythe same function or achieve substantially the same result as thecorresponding embodiments described herein may be utilized according tothe present invention. Accordingly, the appended claims are intended toinclude within their scope such processes, machines, manufacture,compositions of matter, means, methods, or steps.

1. A plate comprising: a first material layer comprising a first stress; a second material layer arranged beneath the first material layer, the second material layer comprising a second stress; an opening arranged in the first material layer and the second material layer; and an extension shaping the opening, wherein the extension comprises a portion of the first material layer and a portion of the second material layer, and wherein the extension is curved away from a top surface of the plate based on a difference in the first stress and the second stress.
 2. The plate according to claim 1, wherein the extension is in its equilibrium position.
 3. The plate according to claim 1, wherein the first material layer comprises a higher compressive stress than the second material layer.
 4. The plate according to claim 1, wherein the first material layer comprises a lower tensile stress than the second material layer.
 5. The plate according to claim 1, wherein the extension comprises a cantilever.
 6. The plate according to claim 1, wherein the extension comprises a plurality of extensions.
 7. The plate according to claim 1, wherein the first material layer comprises a conductive material layer, and wherein the second material layer comprises an insulating material layer, or wherein the first material layer comprises the insulating material layer, and wherein the second material layer comprises the conductive material layer.
 8. A transducer comprising: a membrane; a back-plate comprising an opening, the opening comprising a convex portion, wherein the convex portion is curved toward the membrane; and a spacer between the membrane and the back-plate.
 9. The transducer according to claim 8, wherein the convex portion of the opening comprises an extension of the back-plate.
 10. The transducer according to claim 8, wherein the convex portion is in its equilibrium position.
 11. The transducer according to claim 8, wherein the convex portion is displaced from its equilibrium position when touched by the membrane.
 12. The transducer according to claim 8, wherein the back-plate comprises a conductive material layer and an insulating material layer, wherein the membrane comprises a conductive material layer, and wherein the insulating material layer is arranged between the conductive material layer of the back-plate and the conductive layer of the membrane.
 13. The transducer according to claim 12, wherein the conductive material layer comprises a lower tensile stress than the insulating material layer.
 14. The transducer according to claim 12, wherein the conductive material layer comprises a higher compressive stress than the insulating material layer.
 15. A method for operating a transducer, the method comprising: receiving a sound wave at a membrane; moving the membrane toward a back-plate, wherein the back-plate comprises an opening, wherein an extension shapes the opening, and wherein the extension is curved toward the membrane; and generating a signal in response to the moving membrane.
 16. The method according to claim 15, wherein the extension comprises an equilibrium position if not touched by the membrane, and wherein the extension is displaced from its equilibrium position if touched by the membrane.
 17. The method according to claim 15, wherein moving the membrane toward the back-plate comprises pushing a tip of the extension into the opening.
 18. A method for manufacturing a transducer, the method comprising: forming a membrane in a substrate; forming a back-plate comprising a first material layer and a second material layer, the first material layer comprising a different stress than the second material layer; and forming an opening in the back-plate, the opening comprising an extension extending into the opening, wherein forming the opening comprises etching the opening in the first material layer using a first etch process; and etching the opening in the second material layer using a second etch process.
 19. The method according to claim 18, further comprising causing the extension to bend because of the different stress in the first material layer and the second material layer.
 20. The method according to claim 18, further comprising removing a sacrificial layer between the membrane and the back-plate after the openings are formed.
 21. The method according to claim 20, wherein the removing the sacrificial layer comprises wet-chemical etching or dry etching the sacrificial layer. 